Chapter+4

=toc **Section 1**=

- The part of the roller-coaster that produces the loudest screams is the beginning of the first drop when your stomach feels as though it is falling through you and the roller-coaster picks up immense amounts of speed.
 * What Do You Think:**

__Bizarro:__ Top Speed - 61 mph, Elevation - 14 stories, Duration - 3 mins 15 seconds, Length - 3,985 ft __Nitro:__ Top Speed - 80 mph, Elevation - 23 stories, Length - 5,394 ft, Duration - 3 mins
 * Roller Coasters:**

Distance (scalar quantity) - measured with a flexible piece of string or metric tape measure Displacement - measured distance with a direction included (depends only on the endpoints) Speed - distance traveled divided b the time elapsed Velocity - displacement divded by the time elapsed Acceleration - the change in velocity divided by the time elapsed
 * Physics Talk Summary:**

1. Distance does not include in direction, while displacement does. 2. You're displacement is 2 km. 3. Speed is dependent on distance while velocity is dependent on displacement. 4. You find the change in velocity and divide that by the time elapsed.
 * Checking Up Questions:**

v = 40000/24 v = 1,666.6 km/hr a = 12/3 a = 4 m/s^2 v = 10/2 v = 5 cm/s 5 = 5/t t = 1s a = 25/10 a = 2.5 m/s^2
 * Physics To Go:**
 * 1**.
 * 2**. The first hill on the Terminator Express is the most thrilling because it is the most anticipated and suspenseful to approach.
 * 3**.
 * a:** Bolivia (v=d/t - d= 2(pie)r t= 24h)
 * b:** v = d/t
 * c:** Because it is a constant speed that everywhere and everyone is traveling at all time. There is no change in direction or velocity during it.
 * 4.** a = v/t
 * 5.**
 * a:** speed
 * b:** velocity
 * c:** acceleration - change in direction!
 * d:** displacement & velocity
 * e:** displacement
 * 6.** v = d/t
 * 7.** v = d/t
 * 8**. a = v/t
 * 10.** I would remove both loops and make the hills lower&short (which results in the velocity being less). Also, a larger diameter in the curves for less acceleration.

- On a roller-coaster, the riders experience acceleration during the drops and turns. The parts of the roller-coaster that produce the greatest thrills the first/largest hills along with the different loops (horizontal and vertical). Along with any part with extensive different accelerations or direction changes.
 * What Do You Think Now:**

=Section 2=

- The steel roller coaster would give the bigger thrill because its angle of decent is 90 degrees which would result in a fast velocity and acceleration, along with more a thrill in the drop because they are facing parallel to the ground.
 * What Do You Think:**

- Gravitational Potential Energy: the energy a body possesses as a result of its position in a gravitational field - Kinetic Energy: the energy an object possesses because of its speed - Joule: the SI unit for all forms of energy (kgm^2/s^2 ; Nm)
 * Physics Talk:**

1. The higher the incline, the faster the speed of the ball. 2. When the height increases, the gravitational potential energy does. Along with that, the mass and the GPE also have a direct relation. 3. Kinetic Energy increases as velocity increases. Mass increases, the KE also increases. 4. The GPE loss of energy is transfered to the increase in velocity. 5. As seen in the chart above: 30,000 J of KE
 * Checking Up Questions:**

1. They both have the same speed at the bottom of the track because they both have the same initial height. 3. 4. 5. 6. 7. a: 1.47 J b: 1.47 J c: .375 m (half way) 8. No, because the mass of the cart will not effect the speed of the roller-coaster. GPE = KE (mass cancels on both sides) 9. a: B - because it has the lowest height. b: At C and F because they have the same height. c: D because it has more KE rather than GPE 10 b: H is so much higher because at the top of A that by the time you are halfway through H you have lost all of your KE and will stop moving forward and start moving. 11.
 * Physics To Go:**
 * **Position of Car (height m)** || **GPE (J) = mgh** || **KE (J) = 1/2mv^2** || **GPE +KE (J)** ||
 * top (30 m) || 60,000 || 0 || 60,000 ||
 * bottom (0 m) || 0 || 60,000 || 60,000 ||
 * halfway down (15 m) || 30,000 || 30,000 || 60,000 ||
 * three-quarters way down (7.5 m) || 15,000 || 45,000 || 60,000 ||
 * **Position of car (height m)** || **GPE (J) = mgh** || **KE (J) = 1/2mv^2** || **GPE + KE (J)** ||
 * top (25 m) || 75,000 || 0 || 75,000 ||
 * bottom (0 m) || 0 || 75,000 || 75,000 ||
 * halfway down (12.5m) || 37,500 || 37,5000 || 75,000 ||
 * three-quarters way down (5 m) || 15,000 || 60,000 || 75,000 ||
 * **Position of car** || **Height (m)** || **GPE (J) = mgh** || **KE (J) + 1/2mv^2** || **GPE + KE (J)** ||
 * bottom of hill || 0 || 0 || 50,000 || 50,000 ||
 * top of hill || 25 || 50,000 || 0 || 50,000 ||
 * top of loop || 15 || 30,000 || 20,000 || 50,000 ||
 * horizontal loop || 0 || 0 || 50,000 || 50,000 ||


 * What Do You Think Now:**
 * -** You will experience the more thrill on B because you would experience more acceleration because of the steepness of the track. The speed at the bottom of both tracks will also be the same because both of the tracks have the same initial height.

=Section 3=

- Today, most roller-coasters also start with a "lift hill" with a chain or cable pulling it up to the first drop. It does not cost more to lift the roller-coaster if it is full of people because mass is not a factor in the equation of GPE = KE (the mass cancels out)
 * What Do You Think?**

__Spring Potential Energy:__ the energy stored in a spring due to its compression or stretch - SPE = 1/2kx^2 - GPE + KE + SPE = constant (mgh + 1/2mv^2 + 1/2kx^2 = constant)
 * Physics Talk:**


 * Checking Up Questions:**
 * 1**. The spring potential energy of a "pop-up" toy after it leaps off the table increases
 * 2.** The kinetic energy will be 2J because it has 2J of potential energy.
 * 3.** The GPE will be 2J when it reaches maximum height

(300)(9.8)(15) = electric energy 44,100 J = electric energy KE = 1/2(400)(15^2) KE = 45,000 J GPE = 45,000 J h = 11.48 meters 1/2mv^2 = EPE 1.2(.020)(2.7^2) = EPE .0729 J = EPE 52,920 J = 1/2k(4)^2 6,615 Nm/s = x GPE = mgh GPE = 70,560 J 1/2(6,615)x^2 = 70,560 x = 4.62 m KE = 1/2kx^2 KE = 1/2(40)(.3)^2 KE = 1.8 J
 * Physics To Go:**
 * 5.** The second hill can't be higher than the first because it won't have enough gravitational potential energy to reach the top of the second hill.
 * 6.** Work due to friction creates heat - the thermal energy takes away GPE which makes it less available for Kinetic Energy.
 * 7**. GPE = electric energy
 * 8a.** KE = 1/2mv^2
 * 8b.** GPE = KE
 * 8c**. 45,000 = 400(9.8)h
 * 9.** The GPE increases as the height increases when the ball is thrown upwards.
 * 10.** They both gain the same because they are all going up to the same height so the GPE will is equal at the end (path independent).
 * 11a**. The results are similar (.078 vs. .073)
 * 11b.** KE = EPE
 * 11c.** .4/3 = .13 m
 * 12a**. EPE = 1/2kx^2
 * 12b**. GPE = SPE
 * 13**. KE = SPE

- As mass increased, the pop up toy's height decreases. When the mass of a roller-coaster increases, the GPE needed to pull the roller-coaster also increases. This shows that because a roller-coaster is pulled by cables and electricity that when it's mass increases it needs more electric energy in order to go through the ride at the normal speed. Also, this means that the heavier the coaster is, the more it costs for the company to be able to lift the roller-coaster.
 * What Do You Think Now:**

**Section 4**

- Gravity has a direction - the direction is that it pushes towards the core of the earth. Because gravity is always pushing inwards, people in Australia are able to be held on earth because gravity is always keeping them on the ground.
 * What Do You Think:**

- Field: an influence that one object sets up in the same around it >> Earth is the source of its gravitational field >> The direction of the gravitational field is the direction of the force on a mass >> The gravitational field is stronger where the lines are close together and vice versa >> The gravitational field is present everywhere & extends out to infinity - Response Object: responds to the field & is used to test for the existence of the field and map ing it. - Inverse-Square Relationship - the force of gravity between two objects decreases by the square of the distance between them - Newton's Law of Universal Gravitation - describes the gravitational attraction of objects for one another >> All bodies with mass attract all other bodies with mass >> The force is proportional to the product of the two masses and gets stronger as either mass gets larger >> The force decreases as the square of the two masses between two bodies decreases >> Fg = Gm1m2/r^2 > - Fg is inversely proportional to d^2 > - Fg is inversely proportional to m1(m2)
 * Physics Talk:**

1) Inwards to the center of the classroom 2) The center of the Earth 3) The force of gravity triples 4) Gravitational pull 5) An elliptical path
 * Checking Up:**

1) 1/4 of 500 - 125 N 2) 3) Because we have never not had gravity (it is always present as long as their is mass) 4) Acceleration due to gravity is less at the top than the bottom. 5a) The water side of the earth is closer to the moon 5b) When the body of water is facing the moon, there are higher tides. 5c) As a result of the water on the other side of the earth, farther from the moon, there are lower tides -- uneven distribution. 6a) The fish would break the water bubble it's swimming in and then would result in all fish dying. 6b) Gravity holds the **water** down and as a result the fish can swim in it. 7) a: Force is decreased by 1/4 b: Force is decreased by 1/9 c: Force is decreased by 1/16 d: Force is increased by 4 8) a: Double the force b: Triple the force c: Quadruple the force d: Half the force 9) a: Force is increased by 4 b: Force is increased by 9 c: Force is increased by 16 d: Force is decreased by 1/4 10) a: Force doubles b: Force increases by 9 c: Force increases by 6
 * Physics To Go:**

FG = 1/(3.84x10^8) FG = 2.60916x10 ^-9
 * Physics Plus:**

C = 2πr Time = 2415793158/2440800 v = 988.505 m/s a = 988.505^2/3.84 x 10^2 a = .0025 m/s^2

- Gravity's direction is inwards toward the center of the earth. Australians can be held on the earth even though they are "upside down" because gravity is holding them into the center.
 * What Do You Think Now:**

=Section 5=

- You cannot because the elephant is so much bigger than a canary that it would a) not fit on the scale and b) probably break the scale due to it's heaviness. A bathroom scales is very simple, you just step onto it and it gives you the weight that you are pushing through your feet onto the scale.
 * What Do You Think:**

- Hooke's Law: The restoring force exerted by a spring is directly proportional to the stretch or compression of the spring > Fs = -kx (F is the force of the spring, K is the spring constant and x is the stretch distance, [-] means the force is opposite the stretch of the spring) > Fs = mg [only when a = o] > Slope = K .. small k = more soft / big k = less soft - Weight: The force exerted on a mass as a result of gravity; the weight force on an object due to Earth is downward, in the vertical direction
 * Physics Talk:**

1)The stretch of the spring increased five times as well. 2)The spring constant increases along with the spring stretch and the mass added, it is a constant increase 3)The weight is the mass times 9.8 (acceleration due to gravity) 4)The force of compression of the spring is equal to your weight
 * Checking Up:**

1) a: 100*9.8 = 980 N b: 10*9.8 =98 N c: 60*9.8 = 588 N 2) a: 130*4.45= 578.6 N b: 1000*4.45 = 4450 c: 50*9.8 = 222.5 N 3) a/b: c: Slope of the graph is 14.9 which also is the spring force constant d: This graph line is very steep, meaning that the spring is not very stretchy at all. 4) F = kx 12 = .03k k = 400 (N/m) 5) As the force **increases** so the stretch **increases**. 6) The spring with the k value of 15 N is able to stretch easier 7) 3-1/.02-.007 (rise over run) -- the slope & k value is 153.84 N/m 8) A spring scale works because a certain amount of weight pulls it down. It also depends on how easily stretched the spring is. If a spring is very easily stretched, it takes less weight to stretch down to the same length than a spring that is hard to stretch.
 * Physics To Go:**

- A canary and an elephant cannot use the same scale because the scale with an elephant on it will not be able to register the little change of a small weighed canary. A bathroom scale uses the mass of a person multiplied with acceleration of gravity to give one their weight.
 * What Do You Think Now:**

=Section 6:=

- You're weight does not change when you are on a roller coaster, but the scale would not give different readings at different places.
 * What Do You Think Now:**

Types of Motion: Increasing, Constant, Decreasing __Velocity:__ > acceleration and velocity point in the same direction (increasing) > acceleration and velocity point in the opposite direction (decreasing) > constant speed = acceleration is zero __Net Force:__ > Must be in the same direction as acceleration: ∑F = ma > The bigger force is always pointing in the same direction of ∑F ( FBD diagram)
 * Physics Talk Summary:**

1) The sum is zero 2) The scale reading is greater than the actual weight. 3) The scale is accelerating more weight onto your body (upwards) than the weight of your body motionless (pressing downwards). 4) The scale reading is zero (falling at the same rate that the scale is falling - no push) 5) Air resistance
 * Checking Up:**

1) vf = vi + at a: vf = 0 + 9.8(2) vf = 19.6 m/s b: vf = 0 + 9.8(5) vf = 49 m/s c: vf = 0 + 9.8(10) vf = 98 m/s 2) vf = vi +at a: vf = 0 + 1.6(2) vf = 3.2 m/s b: vf = 0 +1.6(5) vf = 8 m/s c: vf = 0 +1.6(1) vf = 16 3) a: Yes because the lines are both equal and oppositely pushing against the block b: Yes c: Yes 4) **(greater, less or equal to weight)** || 5) The elevator is accelerating downwards. (Increasing down or decreasing up) 6) His/her weight will be larger than 600 N. 7) a: Decrease b: ∑F = ma N - w = ma N = ma + mg N = (50)(-1.5) + (50)(9.8) N = 415 J 8) a: 50 kg - 490 N : N = w = mg b: ∑F = ma N - w = ma N = ma + mg N = 50(2) + (50)(9.8) N = 590 N c: 50 kg - 490 N 9) There is a different scale reading for the student in each elevator because the acceleration or gravitation in each picture is different. When the weight and gravitation are equal (along with acceleration being constant), the scale will read the students normal weight. When the acceleration is down in a free fall, the weight of the person will be zero. When the elevator is accelerating upwards with more energy than gravitation, the scale reads a higher weight. 10)
 * Physics To Go:**
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** || **Relative Scale Reading**
 * At rest, bottom floor || v = 0, a = o, ∑F = o || N = W ||
 * Starting at Rest, Increasing Up || v = up, a = up, ∑F = up || N > W ||
 * Continuing to move, Constant Up || v = 0, a = 0, ∑F = 0 || N = W ||
 * Slowing down to top floor, Decreasing Up || v = up, a = down, ∑F = down || N > W ||
 * At rest, top floor || v = 0, a = 0, ∑F = 0 || N = W ||
 * Starting at rest, Increasing Down || v = down, a = down, ∑F = down || N < W ||
 * Continuing to move, Constant Down || v = 0, a = 0, ∑F = 0 || N = W ||
 * Coming to a stop on the ground floor || v = down, a = up, ∑F = up || N > W ||

- You're weight does not literally change while riding a roller coaster, yet due to the direction of acceleration through out the ride, a scale would have different readings. If acceleration is up, it would read as though you were heavier than your actual weight. If acceleration is down, it would read as though you were lighter than your actual weight.
 * What Do You Think Now:**

=Section 7=

- You don't fall out of a roller-coaster cart when it goes upside down during a loop because their is always centripetal force pulling you in to the center of the circle.
 * What Do You Think Now:**

- Centripetal Force: the force or combination of forces that keep an object moving in a circular motion ; can be normal, tension, weight or friction - Centripetal Acceleration: the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed > equations: a c = v 2 ﻿/r, ∑Fc = mac -∑Fc = mv^2/r > increase mass & increase F (direct relationship) > increase v & increase F (direction square) > increase r & decrease F (inverse relationship) - To find apparent weight: > identify direction acceleration > identify direction of net force > bigger force i the same as ∑F: **always to the center**
 * Physics Talk:**

1) Centripetal Force 2) Yes because you are constantly changing direction 3) Weight and Normal 4) Normal force is responsible for apparent weight. 5) Mass increases - Fc increases ; Velocity increases - Fc increases ; Radius increases - Fc decreases
 * Checking Up:**

1) a:circle - PICTURE b: if the string broke it would be tangent - PICTURE 2) a: Friction - PICTURE b: Leave the circle - PICTURE 6) a: No b: Yes c: vf + -vi N20 + W20 sqrt(20^2+20^2) = 28.3, 45degress 7) v^2/R 20^2/200 =2 m/s^2 10)
 * Physics To Go:**
 * **Fast Roller Coaster** || Required Centripetal Force || Force of Gravity (weight) || Normal Force (force of track on car) ||
 * Top of Loop || 4000 N [mv^2/R] || 500 N || 3500 N ||
 * Bottom of Loop || 6000 N || 500 N || 6500 N ||

13) A: heavier, B: uncertain, C: heavier, D: heavier, E: normal 14) A: UP, B: DOWN, C: UP, D:, UP, E: ZERO, F: SIDEWAYS, G: SIDEWAYS
 * **Slow-Moving Roller Coaster** || Required Centripetal Force || Force of Gravity (weight) || Normal Force (force of track on car) ||
 * Top of Loop || 800 N || 500 N || 300 N ||
 * Bottom of Loop || 2800 N || 500 N || 3300 N ||

1) a: The Net Force decreases in an indirect relationship b: The velocity increases in a direct relationship 2) The track must be at least 4 times stronger 3) The Net Force also decreases with the radius of the curve. 4) The larger the radius for the curve, the **larger** the force required to keep the car moving along the curve. If the curve is tight than a **smaller** force is required. 5) The more string let out into the curve the less force was needed to complete the circle. a: a = v^2/r a = 12^2/20 a = 7.2 m/s^2 b: Fnet = ma Fnet = (300)(7.2) Fnet = 2160 N
 * Physics Plus:**
 * Sample Problem:

- You do not fall out when you go upside down in a roller coaster car because the centripetal force holding you into the circle is large enough to keep you in your seat during the duration of the loop. At the top of a loop, the normal force and the weight are both facing down, which means that net force is also facing down. Also, the radius of the loop is smaller at the top (decreasing velocity) and bigger at the bottom (increasing velocity). The track needs to push on the cart down with a certain amount of force.
 * What Do You Think Now:**

=Section 8=

- There is no more energy needed if the angle of the incline is different because the coaster is still making it up to the same height. It is more difficult to walk up a steep incline than a gentle incline because
 * What Do You Think:**

__Work:__ the product of the displacement and the force in the direction of the displacement; the energy transferred to an obect __Power:__ the work done divided by the time elapsed; the speed at which work is done and energy is transferred
 * Physics Talk Summary:**

1) The energy is in GPE 2) From the kinetic energy 3) The ramp makes it easier and takes less energy. 4) The kinetic energy decreases 5) The unit of power is Watts
 * Checking Up Questions:**

1) a: At the top of the incline, full and at the bottom less b: Work = GPE c: Work = SPE d: SPE = 1/2kx^2 e: Kinetic and a little bit GPE f: when it first hits the spring 2) a: Zero because the directions of the force and the direction of the moving in perpendicular directions b: W = Fd W = 60(.5) W = 30 J c: W = Fd W = 75(40) W = 3000 J d: W = Fd W = 500(.7) W = 350 J 3) Decrease energy consumption, don't waste energy 4) Heavier - more force - more work - more GPE 5) a: W = Fd W = 10,000(20) W = 200,000 J b: P = W/t P = 200,000/150 P = 1,333.3 W 6) There is work up the first incline to get the coaster up to the front, and then GPE energy at the top. During the first drop it's kinetic energy. Vertical loops have GPE and KE. The back curve has little GPE and mostly KE, same the with horizontal loop. At the end there is work due to friction (inverse) to stop the coaster.
 * Physics To Go:**

- It does not take more energy because the top height is still the same. It is more difficult to walk up steep inclines because a person decreases the amount of time it takes them to reach the top, which is results in using more power (watts) to make it up the incline.
 * What Do You Think Now:**

=Section 9=


 * What Do You Think:**
 * -**The parts of the snake that will be the most thrilling are where the turns are the most narrow. This results in a direction and an acceleration. change. Because the turns can be different sizes, the riders still have different thrills through out the ride.

Roller Coaster GPE: - The total mechanical energy (GPE + KE) is the same at everyone point (ignoring friction) - The GPE depends only on the height from a reference position (GPE = mgh) since the mass and the gravitational force remain the same. - If two points on a roller coaster have the same height, the roller coaster is moving at the same speed at those two points. Force (vector quantity): -On the straight incline, gravitational force and the normal force remain in fixed directions. The car has an acceleration that is constant in magnitude and direction. - On the curved line, the normal force changes direction and changes in magnitude (big thrills) - Heights above the ground are the same, GPE is the same. GPE is the same, total energy is the same, the KE is the same. The KE is the same, the speed is the same. __Scalar(size):__ speed, energy, mass, time __Vector (has direction&size)__: force, momentum, acceleration, velocity > Vector Addition: pythagorean theorem to find resultant, use trig functions to find angle > Newtons seconds law and the law of conservation of energy
 * Physics Talk:**
 * Force** in the direction of motion creates **work**, and any **work** done creates changes in **energy**

1) You need to draw it out and the adding/subtracting is dependent on the direction. 2) Energy is scalar, Force is vector. 3) What points are the same height, where the roller-coaster has the same speed and where the roller-coaster has equal energy. 4) Yes because energy depends on the height that the roller reaches along with the speed. 5) Acceleration and turns.
 * Checking Up Questions:**

1) 2) The same GPE at the top of the hills, which means the same speed through out the hill. 3) a: scalar b: vector c: scalar d: vector e: vector f: vector g: scalar h: scalar i: scalar 4) a: Scalar b: Vector c: Scalar d: Vector 5) Energy: when the roller-coaster is moving - when trying to find speeds and you know the heights (vice versa) Force: when you want to find acceleration or normal force 6) a: b: c: Because there are no turns or hills, it is a straight line. The forces are all the same through out the hill. 7) a: b: The total energy is always the same
 * Physics To Go:**

- The parts of "The Snake" that will be the most thrilling at the parts with the most serve direction changes in the turns. Even though the speed is constant, there is still acceleration due to the turns, which causes "The Snake" to remain thrilling.
 * What Do You Think Now:**

=Section 10=

When you know that people could get hurt on a roller coaster, it takes away the thrill of the ride and replaces it with fear. Nobody would ride roller coasters if they knew that 1/2 of the people that went on the rides ended up dying.
 * What Do You Think**

Max acceleration in a curve = 4 g's > v^2/r = 39.2 m/s^2 > greater than 4 g's -- unsafe: change the radius to be bigger or decrease speed (decrease initial height, increase height of the curve), *find a velocity that would be safe Forces (apparent weight) > a = 4g >N = 5g @ bottom of a curve > N = 3g @ top of a curve Minimum Speed Requirement at the top of loop: acceleration greater than free fall
 * Physics Talk**


 * Checking Up**
 * 1) The maximum safe acceleration is 4 g's **
 * 2) Increasing the radius or decreasing the speed **
 * 3) At the bottom **
 * 4) At the bottom **

1) The amount of force at each point of the roller coaster, (GPE and KE), all g's are under 4, track must best be strong enough to hold the forces. 2) a: mgh = 1/2mv^2 9.8(h) = 1/2(20)^2 = 20 m b: a = v^2/r a = 20^2/12 a = 33 m/s^2 c: Yes d: v^2/12 = 39.2 v = 21.6 m/s e: v^2/7 = v =17 m/s 3) a: a = v^2/r a = 62.5 m/s^2 b: No because it is over 6 g's when the appropriate amount of g's is 4 4) a: mgh = 1/2mv^2 9.8(5) = 1/2v^2 = 31 m/s b: a = v^2/r a = 31^2/10 a = 96.1 m/s^2 c: Ac = v^2/r 96 = v^2/10 v = 24 m/s d: 58 m/s e: The acceleration is safe at both the top and the bottom of the link. 5) a: mgh = 1/2mv^2 9.8(16) = 1/2v^2 v = 8.9 m/s b: mgh = 1/2mv^2 9.8h = 1/2(8.9^2) h = 20 m 6) a: a = v^2/r a = 8 m/s^2 b: mv^2/R 900(12)^2/18 = 7200 N c: The track on the wheels 7) a: a = v^2/r a = 26.6 m/s^2 b: mv^2/R 900(20)^2/15 = 24,000 N c: 8) a: No because mass is not a factor in finding centripetal acceleration. b: Same c: Yes because the normal force from the track needs to be greater.
 * Physics To Go: **


 * Physics Plus:**

- Knowing that people can get hurt or die on a roller coaster can result in people being less excited about riding the roller coaster, let alone going on it at all. It takes away the thrill of the coaster and replaces it with thrill. My answer would stay the same if found out that 1/2 of all roller coasters rides ended in the death of it's passengers, I believe that nobody would ever ride roller coasters because the thrill is not worth death.
 * What Do You Think Now:**